1. Field of the Invention
The present invention relates to a method and an apparatus for detecting a rotor angle of a DC brushless motor by superposing a periodic signal over a drive voltage of the motor.
2. Description of the Related Art
To obtain a desired output torque from a DC brushless motor, it is necessary to apply a voltage to an armature at an appropriate phase that matches an electrical angle of a rotor having magnetic poles (hereinafter referred to as a “rotor angle”). There have been proposed various methods for detecting rotor angles without using position detecting sensors so as to achieve reduced cost of a DC brushless motor and a drive unit by obviating the need for the position detecting sensors for detecting rotor angles.
The inventors of the present application have proposed, in a previous application (refer to Japanese Unexamined Patent Application Publication No. 2004-120834), a method in which second-order differences of a d-axis current and a q-axis current are calculated by alternately conducting feedback control only on the d-axis current and feedback control only on the q-axis current, and an estimated value of a rotor angle is calculated by using a second-order difference when the feedback control of current supplied to a DC brushless motor is conducted by so-called dq vector conversion at every predetermined control cycle.
According to the aforesaid method, a sine reference value and a cosine reference value based on the double angle of a phase difference between an actual value and an estimated value of a rotor angle can be calculated by using a calculated value of a second-order difference of d-axis current and q-axis current. Thus, the rotor angle can be detected on the basis of the sine reference value and the cosine reference value.
As described above, the rotor angle of the DC brushless motor can be detected by calculating the second-order difference of the d-axis current and the q-axis current. However, if a second-order difference of the d-axis current and the q-axis current based on a detected value of a phase current is used, then it is expected that a greater detection error of phase current will result, as explained below.
If a detected value of the phase current at an n-th control cycle is denoted by I(n) and a detection error at that time is denoted by N(n), then a first-order difference ΔI and a second-order difference ΔΔI of phase current are given by the following expressions (1) and (2), respectively.ΔI={I(n)+N(n)}−{I(n−1)+N(n−1)}  (1)ΔΔI={I(n)+N(n)}−2{I(n−1)+N(n−1)}+{I(n−2)+N(n−2)}  (2)
If the error N(n) at detection of a phase current is assumed to be a white noise (zero on the average) indicating no correlation to each other, then a variance of the first-order difference (the expected value of a squared error from a mean value) E1 and a variance E2 of the second-order difference are given according to the following expressions (3) and (4) when the variance of error is denoted by σn.
                                                                                             E                  1                                =                                ⁢                                  (                                                            {                                                                        Δ                          ⁢                                                                                                          ⁢                          I                                                -                                                  Δ                          ⁢                                                                                                          ⁢                                                      I                            _                                                                                              }                                        2                                    )                                                                                                        =                                ⁢                                                      E                    ⁡                                          (                                              Δ                        ⁢                                                                                                  ⁢                                                  I                          2                                                                    )                                                        -                                      Δ                    ⁢                                                                                  ⁢                                                                  I                        _                                            2                                                                                                                                              =                                ⁢                                                      E                    ⁡                                          (                                                                        [                                                                                    {                                                                                                I                                  ⁡                                                                      (                                    n                                    )                                                                                                  +                                                                  N                                  ⁡                                                                      (                                    n                                    )                                                                                                                              }                                                        -                                                          {                                                                                                I                                  ⁡                                                                      (                                                                          n                                      -                                      1                                                                        )                                                                                                  +                                                                  N                                  ⁡                                                                      (                                                                          n                                      -                                      1                                                                        )                                                                                                                              }                                                                                ]                                                2                                            )                                                        -                                                                                                                        ⁢                                                      {                                                                                            I                          _                                                ⁡                                                  (                          n                          )                                                                    -                                                                        I                          _                                                ⁡                                                  (                                                      n                            -                            1                                                    )                                                                                      }                                    2                                                                                                        =                                ⁢                                  2                  ⁢                                                                          ⁢                                      σ                    n                                                                                                            (          3          )                                                                                                          E                  2                                =                                ⁢                                  (                                                            {                                                                        Δ                          ⁢                                                                                                          ⁢                          Δ                          ⁢                                                                                                          ⁢                          I                                                -                                                  Δ                          ⁢                                                                                                          ⁢                          Δ                          ⁢                                                                                                          ⁢                                                      I                            _                                                                                              }                                        2                                    )                                                                                                        =                                ⁢                                                      E                    ⁡                                          (                                              Δ                        ⁢                                                                                                  ⁢                        Δ                        ⁢                                                                                                  ⁢                                                  I                          2                                                                    )                                                        -                                      Δ                    ⁢                                                                                  ⁢                    Δ                    ⁢                                                                                  ⁢                                                                  I                        _                                            2                                                                                                                                              =                                 ⁢                                  E                  (                                      [                                                                  {                                                                              I                            ⁡                                                          (                              n                              )                                                                                +                                                      N                            ⁡                                                          (                              n                              )                                                                                                      }                                            -                                              2                        ⁢                                                  {                                                                                    I                              ⁡                                                              (                                                                  n                                  -                                  1                                                                )                                                                                      +                                                          N                              ⁡                                                              (                                                                  n                                  -                                  1                                                                )                                                                                                              }                                                                    +                                                                                                                                                                                                                                 ⁢                                              {                                                                              I                            ⁡                                                          (                                                              n                                -                                2                                                            )                                                                                +                                                      N                            ⁡                                                          (                                                              n                                -                                2                                                            )                                                                                                      }                                            ]                                        2                                    )                                -                                                      {                                                                                            I                          _                                                ⁡                                                  (                          n                          )                                                                    -                                              2                        ⁢                                                                              I                            _                                                    ⁡                                                      (                                                          n                              -                              1                                                        )                                                                                              +                                                                        I                          _                                                ⁡                                                  (                                                      n                            -                            2                                                    )                                                                                      }                                    2                                                                                                        =                                ⁢                                  4                  ⁢                                                                          ⁢                                      σ                    n                                                                                                            (          4          )                    
Thus, it is expected that there will be less influences of the detection error N(n) if the first-order difference is used rather than the second-order difference.